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Davis 

Genetic  construction  work  based 
on  intersecting  planes 


THE  LIBRARY 

OF 

THE  UNIVERSITY 

OF  CALIFORNIA 

LOS  ANGELES 


G 


enctic 


Construction  Work 


BASED    ON 

INTERSECTING    PLANES 

SOUTHERN   BRANCH 

UNIVERSITY  OF  CALIFORNIA 
LIBRARY 

I  '  -?,  CALIF, 


By 

JESSIE   DAVIS 

Instructor  in 
The  Chicago  Kindergarten  College 


Published  by 

THE  CHICAGO    KINDERGARTEN   COLLEGE 
1200  Michigan  Boulevard 


£>54'^<. 


Copyright  1908 

By  JESSIE  DAVIS 

Chicago 


INTRODUCTION 

All  handwork  is  not  educative  any  more  than 
all  books  are  instructive.  Much  time  and  attention 
have  been  wasted  in  many  schools  by  the  so-called 
occupation  work.  Even  much  of  the  handwork 
which  results  in  the  making  of  definite  objects  lacks 
true  educative  value. 

The  importance  of  this  new  handwork  of  Miss 
Jessie  Davis  is  that  it  is  based  on  the  eternal  and 
universal  forms  of  geometry  and  includes  the  funda- 
mental principles  of  all  construction.  It  therefore 
connects  not  only  with  the  industrial  and  art  life  of 
mankind  (leading  directly  into  the  same),  but  it  is 
genetic,  one  kind  of  a  work  growing  out  of  the  mas- 
tery of  the  preceding  kind,  as,  for  example,  the  in- 
tersection of  planes  leads  the  child  to  a  familiarity 
with  diametral  lines.  These  are  the  chief  elements 
used  in  the  second  series  and  thus  is  emphasized  the 
central  point  at  which  the  diametral  lines  meet.  The 
central  point  becomes  a  pivot  around  which  the 
third  series  swings,  and  so  on,  throughout  the  entire 
series. 

Like  all  fundamental  things  this  work  is  exceed- 
ingly simple.    When  rightly  understood,  I  feel  sure 

3 


that  it  will  form  a  strong  bond  between  the  kinder- 
garten and  the  grades  of  our  public  schools,  as  it 
contains  almost  unlimited  possibilities  of  new  forms 
and  combinations,  thus  stimulating  the  creative  ac- 
tivity of  children  from  the  kindergarten  age  to  the 
grammar  grades.  I  need  only  add  that  it  has  been 
thoroughly  tested  with  children  of  various  ages  and 
approved  by  eighteen  training  teachers.  However, 
the  work  itself  is  its  own  best  recommendation.  In 
the  following  pamphlet,  the  first  series,  is  given. 
The  others  will  be  published  in  book  form  later. 

ELIZABETH  HARRISON, 
Chicago  Kindergarten  College. 
Februarv,   1<)0<S. 


Genetic    Construction  Work 

2^>.2  -2- 

THE  Genetic  Construction  Work  is  based  on  the 
intersecting  planes  of  the  Second  Gift.  It  is 
called  Genetic  because  it  is  really  generated  by  these 
intersecting  planes.  They  give  the  principle  of  in- 
tersection, by  means  of  which  the  surfaces  hold  each 
other  together.  Thus  this  construction  work  is  based 
on  an  inner  constructive  principle.  The  intersecting 
planes,  passing  through  each  other,  hold  each  other 
together  and  reveal  not  the  solid,  but  the  constructive 
principle  of  the  solid. 

Applying  this  principle  of  construction,  intersec- 
tion, to  surfaces  in  many  different  ways  we  can  make 
a  variety  of  forms  which  have  the  three  dimensions 
of  a  solid,  but  which  are  hollow.  Most  hollow  forms 
made  by  man  can  be  made  by  the  child  with  card 
board,  through  intersection. 

Thus  the  little  child  can  play  his  way  into  the 
constructive  work  of  mankind.  For  intersection  is 
the  principle  used  by  man.  All  dovetailing,  hinging, 
brick-laying,  mortising,  nailing,  etc.,  are  ways  of  in- 
tersecting surfaces  and  lines  so  that  they  hold  each 
other  together.  And  surely  the  child  is  educated 
through  construction  work,  not  so  much  hy  producing 
the  outer  form  or  object,  as  by  finding  out  and  using 
the  making-poiver. 


The  intersecting  planes  of  sphere,  cube  and  cyl- 
inder are  made  and  cut  for  the  child  in  order  that  he 
may  put  them  together  and  discover  for  himself, 
through  play,  the  principles  of  construction.  The 
child  in  playing  with  them  is  playing  with  the  universal 
principle  of  construction  before  he  makes  the  particu- 
lar object.  This  corresponds  to  the  law  of  develop- 
ment by  which  we  use  the  whole  before  the  parts ; 
the  universal  before  the  particular ;  for  the  particular 
is  generated  by  the  universal.  Moreover,  these  inter- 
secting planes,  being  those  of  the  Second  Gift,  whose 
three  forms  are  two  inches  in  dimension,  show  three 
other  principles  which  will  be  developed  throughout 
this  Genetic  Construction  A\'ork. 

The  first  is  form.  The  circle  and  square  are 
used.  Through  division  other  planes,  the  oblong,  the 
triangle,  the  half  and  quarter  circle  are  produced. 
Thus  we  have  form,  the  plane  with  its  name  to  start 
with.  Not  an  indefinite  surface  is  given  the  child, 
but  a  definite  one ;  for  he  can  not  put  indefinite  sur- 
faces together.     They  do  not  fit. 

The  second  principle  is  measui'emcut.  The 
planes  are  measured.  Just  the  two  inch  circle  and 
two  inch  square  are  given  first — no  other;  for  the 
unit  of  measurement,  one  inch,  is  to  be  developed. 
We  do  not  each  make  this  imit,  and  yet  through  using 
it  each  of  us  remakes  it,  confirms  its  use.  It  is  a 
great  thing  for  a  child  to  begin  to  use  the  same  unit 
of  measure  as  his  race.  He  is  using  the  same  measure 
others  use,  and  thereby  becoming  universal.  But  this 
unit  is  not  directly  given.  Through  division  the  child 
derives  it.     He  re-gives  it  to  himself;  re-makes  this 


measure  which  is  made  and  given  to  him.  The  two 
inch  plane  is  measured,  but  the  child  did  not  do  it. 
By  division  he  can  find  this  unit,  and  so  gain  it  for 
himself,  not  have  it  arbitrarily  given.  xA.lso,  the  two 
inch  size  is  easy  for  little  hands  to  use.  A  one  inch 
size  would  be  too  small,  and  larger,  if  much  larger, 
too  large,  at  least  to  begin  with.  Possibly  a  three 
inch  plane  would  not  differ  much  in  point  of  handling 
from  a  two  inch  one,  but  the  child  could  never 
through  its  easiest  division  reach  the  unit  of  measure. 
The  four  inch  plane  would  require  too  much  division 
to  reach  the  unit  of  measure,  and  would  besides  be 
a  little  too  large.  By  actual  experience,  the  two  inch 
size  is  not  too  small  and  it  enables  the  child  himself, 
through  the  first  and  easiest  division  to  find  the  unit 
-of  measure  which  he  can  now  use  in  measuring  any 
size;  for  three  inch  and  four  inch  planes  are  not 
to  be  kept  from  him.  As  he  becomes  older  and  grows 
in  ability  to  handle  different  sizes,  he  should  use  them 
and  measure  them.  The  two  inch  plane  makes  only  a 
beginning;  but  it  really  makes  the  only  possible  be- 
ginning for  the  development  of  measurement. 

The  third  principle  is  cutting,  which  is  here  in- 
troduced. This  is  more  directly  the  Occupation  side 
of  the  work.  It  is  what  must  be  done  that  these 
measured  surfaces  may  be  divided  and  put  together 
again.  And  measure  is  also  to  be  applied  to  the  cuts. 
They  are  to  be  made  more  and  more  definite  as  the  child 
learns  to  measure,  and  can  cut  the  planes  so  as  to  fit 
better  and  better. 

The  first  cut  is  the  easiest.  One  plane  is  cut,  and 
the   uncut   plane   intersects   the   cut   plane.     The   first 


plane  cut  should  be  a  folded  square.  The  square  is 
folded  once  and  then  cut  from  the  folded  edge  almost 
to  the  open  edges  as  seen  in  Plate  I,  Fig.  1.  This 
cut  is  easy  for  little  children.  It  requires  no  measure- 
ment, and  may  be  cut  quite  near  the  edge  to  which  it 
is  parallel,  or  farther  away.  It  is  well  to  be  satisfied 
with  a  child's  first  cutting  if  it  will  work  at  all. 

In  the  second  cut  both  planes  are  cut  and  inter- 
sect each  other.  This  gives  the  dovetailing,  Plate  I, 
Fig.  2.  This  cut  is  much  more  difficult,  and  demands 
more  ability  to  measure  on  the  part  of  a  child.  The 
two  cuts  must  fit  each  other.  But  although  it  is 
more  difficult,  it  works  better.  The  two  planes  hold 
each  other  more  firmly  in  place,  and  make  a  more 
permanent  object. 

In  the  third  cut  both  planes  are  cut,  one  from 
within  out  and  the  other  from  without  in.  They  in- 
tersect each  other  making  the  hinge,  Plate  I,  Fig.  3. 
This  makes  the  most^  permanent  intersection  of  all, 
as  the  two  planes  when  hinged  can  not  be  pulled  apart. 

The  first  cut  is  a  transitional  one  and  may  gradu- 
ally be  dropped  as  a  child  becomes  able  to  use  the  two 
more  difficult  cuts,  dovetailing  and  hinging.  The  in- 
tersecting with  the  first  cut  does  not  hold  the  forms 
together  very  well ;  although  well  enough  for  a  little 
child  who  is  learning  the  process  of  making  rather 
than  producing  permanent  results. 

All  these  processes  the  child  is  to  play  with  as 
made,  as  universal,  before  he  tries  to  use  them  in 
making  particular  things.     So  the  first  step  is : 

I.     Undirected  Play  with  intersecting  planes. 

It   is    important  that   this   be   given   first,   as   the 


PLATE   I. 

The    Three    Kinds    of    Cuts,    Intersecting,    Dove-TaiHng    and 

Hinging,    With    Application    of    Same 

in    Objects    Made. 


child  should  discover  beginnings  for  himself.  Then 
he  can  be  directed  by  the  knowledge  of  the  past,  by 
the  teacher,  how  to  use  these  discoveries. 

The  first  set  of  intersecting  planes  is  given  in 
the  following  order.  Two  two  inch  circles  already 
cut  to  the  center  are  given  to  each  child.  They  are 
not  intersected  but  lie  on  the  table  apart  from  each 
other.  Let  the  children  pick  them  up  and  put  them 
together  or  do  with  them  whatever  they  wish.  The 
first  thing  they  usually  do  is  to  insert  one  circle  in  the 
cut  of  the  other.  They  do  not  at  once  fit  the  two 
cuts  together,  although  of  course  some  child  might. 
But  they  will  hold  up  one  circle  by  the  other,  will 
say,  "It  makes  a  wheel."  Now  should  begin  a  sym- 
bolic play  with  the  circles,  which  the  kindergartner 
enters  into  being  interested  in  each  new  thing  sug- 
gested, until  at  last  some  child  fits  the  two  cuts  to- 
gether, and  perhaps  begins  to  rock  them,  exclaiming, 
"It's  a  cradle !" 

The  general  experience  with  this  play  has  been 
that  all  the  children  now  try  to  put  their  circles  to- 
gether in  the  same  way,  being  satisfied  with  the  re- 
sults. Now  the  cradles  may  be  rocked,  or  the  planes 
spun  vertically,  suggesting  a  ball  or  anything  else  the 
children  may  think  of. 

Then  laying  the  two  circles  together  and  placing 
them  on  the  center  of  the  table,  give  each  child  two 
two  inch  squares  each  cut  to  the  center.  The  children 
will  at  once  fit  these  together  in  the  same  way  they 
have  discovered  the  circles  will  fit,  and  will  give  to 
the  resulting  figure  various  symbolic  names.  We  now 
have  these  figures — Plate  II.  Fig.  1-2.     Then  let  the 


PLATE  II. 
Geometric    Forms    Made    by    Intersecting    Planes. 


children  take  the  planes  apart  and  see  if  they  can  put 
them  together  again.  Also  they  can  take  each  apart 
and  intersect  circle  with  square,  as  Plate  II,  Fig.  3. 
•Through  this  play  with  the  intersecting  planes, 
the  child  not  only  learns  how  to  intersect,  and  learns 
it  without  direct  teaching,  but  the  forms  themselves 
suggest  to  him  some  of  the  things  he  can  afterward 
make,  as  troughs,  cradles,  shelves,  chairs,  etc.  Then 
by  laying  the  intersected  planes  flat,  they  can  be 
moved  back  and  forth  like  "winding  a  watch,"  as  one 
child  said.  They  can  be  wound  apart  and  then  wound 
together  again.  When  put  away  they  should  be  left 
together. 

Only  two  planes  are  intersected  at  first.  Not 
until  much  later,  especially  with  young  children,  are 
the  three  planes  given,  as  they  are  much  harder  to 
handle.  Besides  they  are  less  symbolic  and  more 
mathematical,  suggesting  at  once  the  intersecting 
planes  of  sphere,  cube  and  cylinder.  When  given,  the 
three  planes  should  be  already  fastened  together  by 
intersection,  but  flattened.  The  child  can  then  pull 
the  parts  out  in  place,  making  the  intersecting  planes. 
Having  done  that,  he  may  then  pull  them  apart  and 
see  if  he  can  put  them  together  again.  It  is  a  little 
too  difficult  for  a  child  to  have  the  parts  separated 
the  first  time.  But  given  in  this  way  he  can  easily  man- 
age them,  taking  apart  and  putting  together.  As  be- 
fore, the  intersecting  planes  of  both  sphere  and  cube 
are  given  at  the  same  time.  The  child  who  can  handle 
the  one  can  handle  the  other.  By  taking  them  apart 
as  before  the  intersecting  planes  of  the  cylinder  can 
be  made  by  the  child.     It  will  doubtless  take  several 


periods  on  different  days  for  the  children  to  exhaust 
the  possibiUties  of  these  planes. 

As  they  suggest  clearly  the  relationship  to  the 
Third  Gift,  it  may  be  brought  out.  The  children  them- 
selves have  frequently  called  for  it  and  have  always 
taken  delight  in  fitting  the  cubes  into  the  corners  of 
these  mtersecting  planes.  If  a  divided  cylinder  and 
divided  ball  are  the  property  of  the  kindergarten  or 
school,  they  will  greatly  add  to  the  interest  and  com- 
prehension of  these  planes,  or  one  might  say,  of 
"the  insides  of  things."  Some  children  have  made 
these  intersecting  planes  at  home  and  brought  them 
to  the  kindergarten,  showing  how  thoroughly  they 
have  understood  them.  But  it  is  not  a  good  plan  for 
the  kindergarten  children  to  be  taught  directly  to 
make  these  intersecting  planes.  If  they  make  the 
planes  crudely  by  themselves,  well  ancL  good ;  but  a 
careful  making  of  them  involves  too  much  measure- 
ment for  a  little  child. 

It  must  not  be  forgotten  that  these  intersecting 
planes  are  to  be  given  through  undirected,  not  directed 
play.  The  forms  suggest  to  the  child  his  own  ex- 
perimenting which  the  teacher  should  follow  and  enter 
into  with  appreciation,  but  should  not  direct.  Also 
this  play  with  intersecting  planes,  whenever  given, 
precedes  the  actual  construction  work  which  is  di- 
rected. They  should  therefore  be  given  the  first  period 
and  the  construction  work  the  second  period.  But 
this  play  with  planes  need  not  precede  the  giving 
of  the  actual  construction  work  each  time.  The  play 
with  two  planes,  circles  and  squares,  should  always 
precede  the  first  giving  of  construction  work,  but  need 


not  the  second.  Indeed  they  need  not  be  given  for 
several  weeks  when  the  children  may  be  ready  to 
discover  new  possibilities  in  them.  And  the  three 
planes  should  not  be  given  until  the  children  are  old 
enough  and  skillful  enough  to  handle  them.  Much 
depends  on  the  teacher,  who  should  understand  when 
her  children  are  ready  to  grasp  both  physically  and 
mentally  each  new  step. 

The  intersecting  planes  form  a  bridge  between 
the  gifts  and  the  occupations.  These  beginning  forms 
are  to  be  made  for  the  child,  played  with  by  him,  and 
returned  unaltered  to  the  box.  This  makes  them 
partly  a  gift.  But  they  are  also  an  occupation,  for 
the  planes  are  put  together,  not  by  external  combina- 
tion, but  by  internal  division.  Used  in  this  way,  they 
form  the  transition  from  the  gifts  into  the  occupa- 
tions. This  transition  is  made  through  the  two  inch 
tablet,  circular  and  square,  which  being  cut  to  the 
center  and  intersected  by  another  tablet  returns  to 
the  Second  Gift  from  which  it  was  derived,  as  it  takes 
up  again  the  dimension  it  lost  as  surface  and  shows 
now  the  three  dimensions  of  the  solid  as  the  three 
intersecting  planes.  And  as  intersecting  planes,  con- 
taining the  principles  of  construction  of  the  solid,  it 
moves  forward  into  the  occupations  through  which 
that  which  is  given  in  the  gifts,  is  to  be  re-given,  re- 
constructed, in  the  occupations  through  surface,  line 
and  point. 

The  present  occupation  reconstructs  the  solid 
through  surface,  and  so  starts  with  giving  the  child 
measured  surfaces  which  he  is  to  learn  to  measure 
and  put  together. 


II.  Directed  Play — intersecting  of  planes  in  vari- 
ous ways. 

The  universal  principle  found  in  the  intersecting 
planes  of  the  Second  Gift,  is  now  to  be  applied  to  the 
making  of  particular  objects.  Also  the  principle 
which  organizes  all  this  directed  construction  work, 
is  the  principle  which  man  uses  in  organizing  all  of 
his  work — and  also  himself:  namely,  measurement. 
"Man  is  the  measure  of  all  things." 

1.  First  Set — objects  made  with  two  inch  planes 
only, — finding  the  unit  of  measure. 

The  first  set  begins  with  two  inch  planes,  circles 
and  squares.  The  first  giving  of  this  directed  con- 
struction work  should  immediately  follow  the  first 
play  with  intersecting  planes.  Two  of  these  inter- 
sected forms,  two  circles  intersected,  and  two  squares 
intersected,  may  be  left  in  the  center  of  the  table  dur- 
ing the  occupation  period,  as  they  serve  to  suggest 
objects. 

Give  each  child  one  two  inch  circle  and  a  pair 
of  scissors.  Have  each  child  fold  the  circle  once 
in  the  middle  and  rock  it  like  intersected  circles.  Then 
open  and  see  the  dividing  diametral  line.  The  divi- 
sion which  the  intersected  planes  suggest  is  now  made 
by  the  child.  Next  he  is  to  complete  what  is  begun. 
The  dividing  diametral  line  is  used  for  division.  Let 
the  children  cut  on  this  folded  line.  In  order  to 
cut  well,  the  fold  should  be  smoothed  out  and  then  cut. 
Never  cut  on  a  fold  doubled  up.  It  always  makes 
poor  edges,  and  admits  of  little,  if  any,  improvement. 
And  besides  this,  the  child  should  see  the  line  he 
cuts  on.     The  folded  line  has  this  advantage  over  the 


drawn  line,  in  that  the  child  can  feel  it  as  well  as  see  it. 
And  again,  he  can  easily  fold  a  line,  a  straight  one, 
whereas  it  would  be  more  difficult  to  draw  a  good 
true  line. 

Now  we  have  two  half  circles.  Then  fold  a 
square  in  the  same  way.  As  the  folded  circle  would 
rock,  so  the  folded  square  will. look  like  a  part  of  the 
intersected  squares.  Now  the  folded  square  is  to  be 
cut  up  each  side  from  folded  edge  toward  open  edges, 
using  the  first  cut.  By  intersecting  in  these  cuts  the 
two  half  circles,  a  cradle  is  made.    Plate  I. 

If  the  kindergartner  precedes  each  process  of 
folding  and  cutting  on  the  part  of  the  children,  by  a 
play  of  intersecting — interlocking  the  fingers,  and 
finally  by  having  the  children  fasten  their  hands  be- 
hind their  backs  in  this  position,  while  she  quickly 
and  definitely  shows  them  how  to  fold  and  cut,  she 
will  find  it  an  easy  way  of  directing.  And  if  she 
keeps  her  own  hands  fastened  in  the  same  way  while 
the  children  fold  and  cut,  helping  no  one  until  all 
have  tried,  she  will  find  it  will  help  the  children  to  be 
independent.  It  is  also  a  good  plan  to  say,  "Can 
you  each  make  another  cradle?"  And  without  direc- 
tion hand  each  child  another  circle  and  square,  letting 
them  make  another  cradle  all  by  themselves.  Little 
children  have  taken  great  delight  in  making  three 
or  four  in  this  way,  and  have  done  it  well. 

Then  holding  up  a  square,  fold  and  cut  in  half 
as  the  circle  was  cut.  Let  the  children  do  the  same. 
Then  give  each  child  a  square  to  fold  and  cut  up 
the  sides  as  before,  making  the  first  cut.  Let  the 
children    intersect   these   oblongs    in   the    cut    square, 


finding  out  what  they  can  make.  Children  no  older 
than  four  years  have  made  four  or  five  forms  this 
way  in  half  an  hour.  Most  of  them  are,  of  course, 
repeated,  the  children  making  several  of  the  same 
form.  This  first  making  of  objects  may  be  carried 
as  far  in  one  period  as  the  children  are  able  to  do  the 
work. 

The  second  time  the  construction  work  is  given 
it  need  not  be  preceded  by  the  play  with  intersecting 
planes.  This  time  the  children  should  make  the  same 
things  as  before,  aiming  now  at  better  work.  A  whole 
half  hour  can  be  well  spent  in  making  one  good  cradle, 
throwing  away  mistakes.  Have  a  small  paper  doll, 
less  than  two  inches  long  to  sleep  in  the  cradle.  To 
this  construction  work  is  thus  added  free-hand  cut- 
ting, for  the  children  can  cut  out  their  own  toys  to 
go  with  the  furniture.  Or,  if  the  teacher  cuts  out 
the  dolls,  the  child  can  cut  out  the  covers  to  put  over 
them,  or  carpet  for  the  cradle  to  rest  on.  Thus  he 
puts  the  things  he  makes  to  a  real  utilitarian  use, 
and  also  becomes  better  able  to  use  the  scissors.  To 
the  cradle  might  be  added  a  chair  for  the  mother  to 
sit  in. 

In  this  first  set  of  two  inch  planes  the  circle  and 
square  are  used  together.  At  first  they  are  cut  only 
in  halves,  the  new  planes  thus  obtained  being  the 
half  circle  and  the  oblong.  Later  they  can  be  cut 
into  quarters.  In  this  way  the  child  makes  his  new 
planes  from  the  old  and  that  too  by  the  simplest 
divisions.  With  a  circle  and  square  and  their  divi- 
sions, a  number  of  forms  can  be  made ;  in  fact,  almost 
all    household    furniture,    as    well    as    houses,    sheds, 

17 


troughs,  and  many  things  used  out  of  doors.  See 
Plate  III. 

But  the  Hmitation  of  the  two  inch  planes  is  their 
size.  All  the  things  made  are  about  the  same  size, 
and  the  objects  when  grouped  together  lack  propor- 
tion. However,  in  this  they  correspond  to  the  little 
child  who  also  lacks  the  sense  of  proportion,  and 
must  learn  it. 

2.  So  the  Second  Set  is — any  inch  plane, — 
using  the  unit  of  measure. 

As  soon  as  the  child  is  ready,  the  step  is  taken 
to  the  next  set  which  is,  objects  made  with  any  inch 
plane.  Now  we  can  use  three,  four  and  five  inch 
circles  and  squares  w'ith  their  divisions.  Beyond  five 
inches  it  is  not  well  to  go,  as  the  paper  used  at  first  is 
necessarily  easily  folded  or  the  child  could  not  handle  it. 
If  too  large  a  plane  is  used  the  object  will  not  stand 
up  well.  To  these  circles  and  squares  are  added  ob- 
longs of  any  length  or  width  as  2x3,  4x5,  etc.  The 
planes  are  divided  into  halves  and  quarters  as  in  the 
first  set. 

The  same  objects  made  in  the  first  set  can  now  be 
made  in  tHe  second.  This  gives  opportunity  for  repe- 
tition, and  also  for  better  work,  and,  more  than  all, 
difiference  in  size.  The  same  things  can  be  made 
larger  or  smaller.  Now  the  tables  and  chairs  are  not 
the  same  height,  but  can  be  proportioned. 

The  child  is  thus  to  progress  in  doing  better  work. 
The  cradle  made  in  the  first  set  has  not  a  flat  bottom, 
being  folded  only  once.  But  the  cradle  made  in  the 
second  set  of  larger  size  can  be  folded  three  times, 
giving  a  flat  bottom  and  so  a  better  cradle.     One  of 

ts 


PLATE   III. 
Two-Inch   Measurement. 

19 


the  things  which  can  be  made  much  better  in  the 
second  set  than  the  first,  is  a  rocking  chair.  To  make 
this,  the  seat  can  be  the  oblong  from  a  two  inch 
square,  and  the  rockers  the  quarters  of  a  three  inch 
circle.  This  gives  a  proportion  to  the  curve  which 
brings  it  far  enough  below  the  seat.  See  Plate  IV. 
The  rocker  made  in  the  two  inch  set  is  not  good,  yet 
it  satisfies  a  little  child  in  his  first  attempts.  These 
two  sets  are  very  closely  connected,  the  same  objects 
being  made  in  each,  and  the  principle  of  the  inch 
measure  underlying"  both. 

By  providing  for  the  making  of  simple  crude 
forms  at  first,  we  give  to  the  child  the  opportunity 
to  do  what  he  can.  And  by  providing  for  a  gradual 
development  through  measurement,  by  which  the  same 
object  can  be  better  and  better  made,  we  provide  for 
the  development  of  the  child's  growing  ability.  He 
can  and  should  grow  out  of  crude  beginnings,  and 
learn  to  do  better  work.  But  also,  he  must  begin 
with  the  crude. 

In  the  first  two  sets  the  child  has  been  using  the 
inch  measure,  becoming  familiar  with  it,  but  not  actu- 
ally measuring  much  himself,  so  the  next  set  must  pro- 
vide for  that. 

3.     Third  Set — any  plane — relative  measurement. 

In  this  set  new  forms  can.  be  made  for  which  the 
first  two  sets  do  not  provide.  Give  each  child  a  four 
inch  square.  Let  him  fold  it  three  times.  Stand 
the  resulting  form  on  end,  so  that  it  looks  like  a 
cupboard  without  shelves.  It  will  be  four  inches 
high,  two  inches  wide,  and  one  inch  deep.     Give  each 


PLATE  IV. 
Any   Inch    Measurement. 

21 


child  a  two  inch  square,  which  he  is  to  fold  once 
and  cut  in  half.  There  will  then  be  oblongs  2x1. 
These  oblongs  fit  exactly  in  the  cupboard  as  shelves, 
but  cannot  be  intersected.  So  the  oblong  cannot  be 
used  as  a  shelf,  but  it  can  be  used  as  a  measure.  Lay 
it  on  another  paper  and  cut  out  shelves  of  the  same 
width  but  a  little  longer  at  each  end,  as  Plate  V. 
As  many  shelves  as  desired  may  be  cut  in  this  way. 
Then  laying  the  measure  on  several  shelves  cut  half 
way  along  each  side  close  to  measure.  The  shelves 
should  now  fit,  having  been  measured  to  fit.  Fold 
over  the  cupboard  part  on  center  fold.  Cut  from 
without  (open  edges)  in  half  way  to  fold.  Inter- 
sect shelves  by  dovetailing.  By  cutting  cupboard 
from  within  out  half  way  beyond  the  fold,  the  shelves 
can  be  intersected  from  the  back.  This  gives  oppor- 
tunity to  put  on  a  door  in  front  by  hinging.     Plate  V. 

From  these  two  cupboards  by  modification,  can 
be  made  all  articles  of  furniture  having  shelves  ;  as 
wardrobes,  bureaus,  writing  desks,  chiffoniers,  also 
using  two  end  shelves  only,  all  sorts  of  boxes  with  or 
without  lids.     See  Plate  A^. 

Also  the  house,  which  can  be  made  with  the 
measured  planes,  can  be  better  made  by  using  this 
principle  of  relative  measurement.  It  can  be  made 
as  wide  or  as  narrow  as  desired,  and  so  any  kind  of  a 
house  is  made.  By  using  the  third  cut,  a  door  can  be 
hinged  on,  and  a  floor  put  in.    Plate  VI. 

As  the  child  learns  to  measure  his  own  planes, 
he  can  learn  also  to  cut  them ;  to  measure  them,  and 
thus  to  apply  his  own  measuring  in  making  over  pre- 
vious sets. 


PLATE  V. 


23 


Inventing  can  be  begun  very  early  with  this  work. 
First,  let  the  children  try  other  ways  of  intersecting. 
They  may  produce  forms  already  made  by  themselves 
as  well  as  new  ones.  Second,  they  can  transform  ob- 
jects made  by  modifying  them  so  as  to  look  more 
like  chairs,  tables,  etc. ;  as,  by  cutting  out  the  legs  to 
chairs,  cutting  out  the  rockers  to  rocking  chairs,  etc. 
See  Plate  Yl.  Everything  a  child  makes  with  the 
planes  can  be  thus  modified,  and  thus  become  his  own 
invention.  Also,  older  children  will  study  new  ways 
of  using  the  methods  of  intersecting;  new  ways  of 
fastening  planes  together. 

III.     Self-Directed  Work — Proportion. 

In  this  last  work  come  the  sets  of  furniture, 
houses,  barns  with  fences  and  other  surroundings. 
Now  a  table  may  be  made,  and  chairs  to  go  with  it. 
A  house  with  fence,  a  barn  with  fence  and  other 
buildings,  etc.,  can  be  made. 

These  sets  are  an  application,  made  by  the'  child, 
of  the  principles  of  making  things,  to  the  grouping 
of  these  things  together.  It  varies  from  the  small 
trough  surrounded  by  a  fence,  or  the  cradle  with  a 
chair  beside  it,  to  all  the  complex  furnishings  of  rooms. 
It  varies  from  the  work  a  four  year  old  child  can 
do,  to  work  that  would  test  the  skill  of  a  grammar 
grade  pupil.     See  Plates  VII,  VIII,  IX. 

In  this  work  the  children  receive,  through  meas- 
urement, a  mathematical  training  which  will  greatly 
aid  their  abstract  number  work.  They  will  gain  skill 
of  hand  through  cutting,  and  develop  inventive  power 
in  fastening  the  planes  together.  They  will  learn  to 
observe    how    things    are    made    in    the    world    about 


PLATE  VI. 
Any  Inch  Planes,  Modified. 

25 


them.  And  finally,  owing  to  the  constructive  prin- 
ciple of  intersection,  and  the  use  of  the  inch  measure, 
this  work  will  make  a  good  preparation  for  the  later 
Manual  Training.  And  more  valuable  still,  it  helps 
the  child  to  understand  the  work  of  man. 


MATERIALS   USED 

A  heavy  paper  should  be  used.  It  must  be 
flexible  enough  to  fold  easily,  yet  stiff  enough  to 
hold  its  shape.  Prang's  Construction  Paper  has  been 
found  to  answer  the  purpose  very  well.  Heavy 
manilla  drawing  paper  may  be  used  for  a  while  in 
the  first  work.  But  it  is  hardly  stiff  enough  for  good 
work,  and  besides  lacks  color  to  make   it  attractive. 

In  the  later  work  of  making  sets  of  objects,  a 
heavier  paper  than  Prang's  is  desirable,  and  more- 
over the  child  will  begin  to  want  a  more  permanent 
material  than  the  Prang's  Construction  Paper.  Sheets 
of  stiffer  paper  will  enable  the  older  child  to  do  more 
satisfactory  work. 

TOOLS    USED. 

Good  scissors  are  necessary,  for  no  one  can  do 
good  work  with  poor  tools.  The  scissors  should  be 
small  and  blunt.     No  paste  or  glue  is  used. 


PLATE  VII. 
Objects  Made  in  Relative  Proportion. 

27 


PLATE  VIII. 
Proportion    Shown   in   Groups   of   Furniture. 


r^    1- 


L^ 


OUTLINE 


GENETIC   CONSTRUCTION  WORK 


I.     Undirected — Play  with  intersecting  planes. 

II.     Directed — ^Measurement. 

1st  Set — Two  inch  planes  used, — tinding  unit 
of  measurement. 

2nd  Set — Any  inch  planes  used, — using  unit 
of  measurement. 

3r(l  Set — x^ny  plane  used.— relative  meas- 
urement. 

Self-directed — Proportion, — making  of  sets  of  ob- 
jects proportioned  to  each  other. 


Outline  of  Kindergarten  Occupations 


I  Moulding 
Plastic,     -{        of 
(forma-      I   material, 
bility)         I, 


Utilitarian. 

Mathematical. 

Artistic. 


■      II. 

Indus- 
trial, 
form- 
making 


r  Utilita- 
rian. 


^  Mathe- 
matical. 


L  Artistic. 


\  Industrial 
I      processes. 


1.  Taking  apart. 


-!  2.  Putting  to- 
gether. 


3.   Both. 


(  Pricking. 
-;  Tearing. 
/  Cutting. 

^  Pasting. 

Sewing. 

(  Weaving. 

-i  Folding. 


Quantitative 
occupations. 


Qualitative 
occupations. 


Quantitative 

and 
Qualitative. 


Occupations 
based  on 

1.   Intersecting  j  Genetic    con- 
plane.  /       struction. 


2.   Diametral 
line. 


(  Transformation 
(      of  one  surface. 


3.  Central 
point. 


i.  point.  /  Wheel  making. 

(  1.   Point  making — pricking. 

^  2.  Line  making — sewing. 
I 
I  3.   Surface   making — weaving. 


Color  work. 


f  Form   used — -Quantitative. 


Making  of  ob-  | 

jectsbasedon  J  How   used— Qualitative, 
mathematical 
principles.  | 

L  Color  used. 


III.         f  r  Utilitarian. 

Graphic,   i  ,  .         i  Mathematical, 

form-  I  making.     | 

revealing.  I.  L  Artistic. 


JAN  1 1  taeo 


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